Dataset DOI: 10.5061/dryad.sn02v6xh8

File list

• Algebra_Equation_Solving_Performance_Using_Hands-On_Equations_Manipulatives_(Grades_6-8).csv
• LD_Study_SAV_File.sav
• Borenson_LD_Study_Output_File.pdf

File descriptions

Algebra_Equation_Solving_Performance_Using_Hands-On_Equations_Manipulatives_(Grades_6-8).csv– the data in unformatted form.

LD_Study_SAV_File.sav– the data for direct use in SPSS.

Borenson_LD_Study_Output_File.pdf- results from statistical analysis (see Output file description under Usage Notes for further information).

Usage Notes

Datafile Description

• Variables/Columns:
  • Nr: Anonymized unique identifier for each student.
  • pretest: Score (0-6 points) on the initial algebra assessment administered before instruction.
  • posttestM: Score (0-6 points) on the post-instructional algebra assessment administered after six lessons using manipulatives.
  • posttestWM: Score (0-6 points) on the final post-instructional algebra assessment administered after the seventh lesson (paper and pencil solution).
  • Grade: Student's grade level (6, 7, or 8).
  • LD: Categorical variable indicating class type (Regular =0 or LD=1).
  • Classroom: Anonymized unique identifier for each classroom.
  • dif1:  posttestM-pretest.
  • dif2: posttestWM-pretest.
  • filter_$ = Categorical variable that can be used to select Grade 7 (value = 1).

Output File Description

This document (Borenson_LD_Study_Output_File.pdf) presents the statistical analysis results generated from the dataset. The analysis includes descriptive statistics, nonparametric tests (Mann-Whitney U Test and Kruskal-Wallis Test), and Friedman's Two-Way Analysis of Variance by Ranks, along with related pairwise comparisons and effect sizes. The document is organized into several sections, each detailing different statistical outputs:

Descriptive Statistics (Pages 1-3)

• Provides summary statistics for pretest, posttestM, and posttestWM variables.
• Breakdown of descriptives by Classroom (1.00 to 8.00) and LD (0.00 and 1.00).
• Includes:
  • N: Sample size for each group.
  • Minimum: Lowest observed value.
  • Maximum: Highest observed value.
  • Mean: Average score.
  • Std. Deviation: Measure of data dispersion.
  • Skewness: Measure of asymmetry of the probability distribution.
  • Kurtosis: Measure of the "tailedness" of the probability distribution.

Nonparametric Tests: Mann-Whitney U Test (Pages 3-5, 27-30, 34-38, 42-44, 64-65)

• This test is used to compare differences between two independent groups on a continuous or ordinal dependent variable.
• Comparisons:
  • pretest, posttestM, posttestWM are compared across LD groups (0.00 vs. 1.00) for different Grade levels (6.00, 7.00, 8.00).
  • pretest, posttestM, posttestWM are compared across Classroom groups (e.g., 4.00 vs. 6.00, 4.00 vs. 5.00, 5.00 vs. 6.00) for Grade 7.00.
  • dif1 and dif2 are compared across LD groups (0.00 vs. 1.00).
• Outputs include:
  • Ranks: Mean Rank and Sum of Ranks for each group.
  • Test Statistics: Mann-Whitney U, Wilcoxon W, Z-score, Asymptotic Significance (2-tailed), and sometimes Exact Significance.

Nonparametric Tests: Kruskal-Wallis Test (Pages 5-18)

• This test is used to compare differences between three or more independent groups on a continuous or ordinal dependent variable.
• Comparisons:
  • pretest, posttestM, posttestWM are compared across Classroom categories for Grade 6.00 and 7.00.
• Outputs include:
  • Hypothesis Test Summary: States the null hypothesis and the decision (Reject/Retain).
  • Test Statistics: Chi-Square, Degrees of Freedom (df), Asymptotic Significance.
  • Pairwise Comparisons: If the overall test is significant, this table provides comparisons between specific classroom pairs with adjusted significance values (Bonferroni correction).
  • Continuous Field Information/Histograms: Visual distribution of scores for pretest, posttestM, posttestWM by grade.
  • Categorical Field Information: Counts per classroom within a grade.

Nonparametric Tests: Friedman Test (Pages 44-45, 47-55)

• This test is used to compare three or more related (dependent) samples, typically within-subjects comparisons (e.g., pretest vs. posttest on the same individuals).
• Comparisons:
  • pretest, posttestM, and posttestWM are compared within each Classroom (4.00, 5.00, 6.00).
• Outputs include:
  • Ranks: Mean Rank for each variable within classrooms.
  • Test Statistics: Chi-Square, Degrees of Freedom (df), Asymptotic Significance.
  • Kendall's W: Coefficient of Concordance, indicating agreement among ranks.
  • Pairwise Comparisons: If the overall test is significant, this table provides comparisons between the three measures (pretest, posttestM, posttestWM) with adjusted significance values.

T-Test and Effect Sizes (Pages 65-66)

• Group Statistics: Provides means, standard deviations, and standard errors for dif1 and dif2 by the LD grouping variable.
• Independent Samples Test: Conducts an independent samples t-test to compare dif1 and dif2 between the two LD groups.
  • Includes Levene's Test for Equality of Variances.
  • Provides t-statistic, degrees of freedom, significance (one-sided and two-sided), mean difference, and confidence intervals.
• Independent Samples Effect Sizes: Calculates effect sizes (Cohen's d, Hedges' correction, Glass's delta) for the differences in dif1 and dif2 between the LD groups, along with their confidence intervals.

The Six Questions of Each Test